I can't think of any "general" war movie which has non-white characters whose ethnicity isn't specifcially tied to the narrative.
That's an unavoidable outgrowth of segregated units during the war. Any movie featuring a segregated unit is going to deal with their race. In fact "Go For Broke" about the 442nd RCT is in production right now. They are the most decorated combat unit in U.S. military history, and all Japanese-American.